Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2598 conjugacy classes of subgroups; only the 752 normal subgroups are shown.
This group has 2598 conjugacy classes of subgroups — too many to draw. Only its 752 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #95×#6157 | C2 | semidirect |
| 6. C4×C22⋊#6157 | C4 | semidirect |
| 9. C2×#13133124 | C4 | semidirect |
| 10. #95×D53 | C4 | semidirect |
| 12. C2×#95×C53 | C4 | semidirect |
| 16. C2×C4×#6157 | C2×C4 | semidirect |
| 17. (C2×#6157)⋊C4 | C2×C4 | semidirect |
| 37. C22×C4×C53 | C42 | semidirect |
| 40. C22×Dic53 | C42 | semidirect |
| 45. C2×C4×D53 | C42 | semidirect |
| 48. C22⋊#6157 | C42 | semidirect |
| 109. C2×#95 | #6157 | semidirect |
| 110. C53 | #13749 | semidirect |
| 144. C22×C4 | C4×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊#6157 | 2 |
| #95×#6157 | 2 |
| C2×#95×D53 | 2 |
| #13749 | 53 |